Griffiths phase and nontrivial collective behavior in dynamical networks - Velez Rojas, Juan Sebastián (2023)
We investigate the occurrence of the novel phenomenon of chaotic Griffiths phase in coupled map networks. In this phase, the distribution of sizes of synchronized clusters follows a power law, not just at a critical value of a parameter, but on a broad range of parameters. We search for the underlying mechanisms that can give rise to a chaotic Griffiths phase in a coupled chaotic map networks by using different map dynamics. We find that a chaotic Griffiths phase appears in networks possessing neuron-based dynamics; thus supporting the view that this phase can play a relevant role in the critical behavior observed in neural systems and brain dynamics. We introduce a statistical quantity that measures the dispersion of clusters in order to characterize the chaotic Griffith phase in dynamical networks. We employ a heterogeneity measure to characterize the dispersion of the parameters of the local maps. We unveil that heterogeneity in either the network topology or in the parameters of the dynamical elements are crucial ingredients for the emergence of the chaotic Griffiths phase.